Long term international cooperation is hard
And it might not come with only advantages, such as share the assembly and operational costs, share science, technology, infrastructure, services, increase IP portfolio and so on.
Some disadvantages are apparent since the Crimea crisis and US/EU sanctions against Russia, when momentarily, even the immediate future of the station wasn't clear and politics and hiccups in diplomacy nearly got the better of it. Additional multilateral reassurances were needed to continue with operations as previously agreed on, and US didn't have to recall all of its personnel from Star City in Russia, Baikonur in Kazakhstan,...
US side isn't exactly guilt-free when it comes to operational complications either. Remember the Government shutdown of 2013 when most of NASA's operations were cut to bare minimum and 97% of its employees on unpaid leave due to US Congress failing to reach an agreement on the FY2014 budget in time? Sure, we all read that ISS operations won't be affected, and to a large degree they probably weren't. But a lot of background work related to ISS activities, including international cooperation, also went on a forced hiatus, for lack of a better word.
So politics often can get in the way of research, and in an international theater, even more frequently so. But there's other points. One is definitely legal, better said - no shared liability; every nation party to the joint international project is equally and individually liable for any and all damages to property or land of other nations. At least that's according to the Outer Space Treaty and the later signed and ratified Space Liability Convention. This additionally complicates such deals between nations, sometimes, it might render them unworkable - but we don't read all that much about projects that failed before they were even established in the press, so this is hard to quantify.
Another point is of difficulties involved with bailouts once the international contracts are signed. Politics change, even their leaders and the whole bandwagon. But you might be stuck with a contract that you later don't like. Our ideas about space exploration change, our needs for their science products change, or we simply want to do the same more efficiently, reshuffle things around a bit. International contracts that hold a large part of your budget hostage might prevent all that, or delay its progress - again, possibly rendering it as a fruitless endeavor.
And finally, security problems. Let's not even mention interdependency and possible obstructions in case one of the nation parties can't or won't fulfill contract obligations. That's another issue altogether, but there are more pressing security concerns such as access control to proprietary or classified technology, and so on in an internationally shared location.
I'm not saying that all of these problems can't be worked with, or some bypassed altogether. There's absolutely also perks to international projects like ISS is, but long term international cooperation is hard. ISS taught us valuable lessons in this regard, still does, and will continue to do so while its fate isn't exactly set in stone and each member state continues to present different, sometimes incompatible ideas of its future.